[seqfan] Re: Fwd: A nice (decimal) property of 78
Maximilian Hasler
maximilian.hasler at gmail.com
Sat Nov 8 23:27:54 CET 2008
Sorry all,
I just noticed a kind of bug in my program below:
Obviously, it prints those n for which
sigma( n ) == sigma( [n/p] )*sigma( n % p ) for some p=10^k
(% = binary "mod" operation)
but this means that n = concat( a, b ) with maybe leading zeroes in b,
which was not really intended.
Apologies,
Maximilian
> there is already the single digit version:
> A098771 Numbers n such that sigma(n)=sigma(d_1)*sigma(d_2)*...*sigma(d_k)
> where d_1 d_2 ... d_k is the decimal expansion of n.
> 1, 2, 3, 4, 5, 6, 7, 8, 9, 38, 58, 66, 87,...
>
> the ( a || b ) version can be computed as follows:
>
> is_sig(n)={ local(p=1, s=sigma(n)); while( n>p*=10, n%p | next;
> s==sigma( n\p )*sigma( n%p ) & return(1))}
> for(n=1,9999, is_sig(n) & print1(n","))
>
> 38,58,66,87,118,178,205,217,275,295,298,395,451,478,492,517,538,575,660,718,766,775,838,839,870,898,1018,1138,1175,1195,1318,1671,1678,1775,1795,1975,2050,2163,2170,2295,2395,2518,2578,2638,2665,2750,2818,2875,2950,2995,2998,3118,3175,3567,3635,3775,3837,3857,3875,3894,3898,3950,3998,4163,4175,4195,4198,4378,4510,4618,4645,4667,4678,4692,4775,4798,4862,4875,4918,4920,4994,5098,5170,5218,5578,5609,5638,5750,5786,5875,5878,5896,5907,5938,5944,5975,5998,6178,6418,6505,6557,6598,6600,6775,6778,7195,7438,7660,7678,7750,7978,8057,8058,8098,8278,8390,8578,8616,8668,8700,8818,8975,9185,9298,9591,9635,9646,9682,9725,9745,9778,9838,9879,
>
>
>> The problem is, in order to prove there are an infinitude of primitive
>> solutions, you generally have to exhibit and infinite family of primitive
>> solutions. But then only one member of the family is primitive, the others
>> become nonprimitive members of the family.
>
> well, for pythagorean triples there are definitions that make sense.
> but I agree that here it does not make much sense to disallow trailing
> zeroes of the 2nd half, b, but allow them for the 1st part, a.
>
> Maximilian
>
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